Finite element simulation modeling permits to predict hydrogen concentration for various initial boundary-values problems, but the results depend on the underlying transport mechanisms accounted for. Trapping process is a key factor in the apparent hydrogen diffusion, and the case of mobile traps as dislocations needs modification of the hydrogen transport equation usually considered in the literature. An extension of this model is proposed where hydrogen dragging by mobile traps is modeled by reaction-diffusion equations, involving trapping and detrapping kinetic, and is applied for evolving trap density with plastic strain. The consequences of trapped hydrogen mobility on diffusive hydrogen repartition in a reference Small Scale Yielding configuration are focused on, especially in term of acceleration of hydrogen transport. The potentiality of the model is illustrated by the modeling of the trapped hydrogen breakaway from fast moving dislocations.